Dynamic response optimization of structures with viscoelastic material using the equivalent static loads method

Viscoelastic material is widely used in automotive structures due to its outstanding vibration-damping characteristics with appropriate stiffness. Viscoelastic material, which has viscosity and elasticity, shows energy absorption and dissipation. The material properties of viscoelastic material are dependent upon time, temperature, and loading path. Hence, these characteristics have to be considered when performing structural optimization. Studies on the constitutive equations of viscoelastic material are widely carried out, and structural optimization using harmonic excitation in the frequency-domain is often reported. However, structural optimization in the time-domain is rarely performed. One of the reasons is that the cost of sensitivity analysis is quite expensive. The Equivalent Static Loads Method (ESLM) is a linear/nonlinear dynamic response structural optimization method. In this research, a practical structural optimization method to consider the characteristics of viscoelastic material is proposed using ESLM. Equivalent static loads (ESLs) are defined as the static loads that generate the same displacement field as that from dynamic analysis. In ESLM, dynamic analysis and linear static response optimization are alternatively repeated until convergence is achieved. Viscoelastic material reduces the vibration amplitude and the stored energy in a structural system. Thus, excellent damping performance is required for a part with viscoelastic material, while the proper stiffness is maintained. An appropriate design formulation is made for the design of viscoelastic material. In this research, the sum of damping ratios, the sum of weighted damping ratios, and the sum of squared displacements are considered as the objective functions. These three objective functions deal with the peak displacements of damped vibration. Three case studies are defined by optimizations of some typical automotive parts with viscoelastic material. They are a sandwich panel, a rubber bushing, and a seat cushion. The damping performances of the objective functions are compared and discussed.

Crash optimization considering the head injury criterion

In the crashworthiness of the vehicle, the head injury criterion is the most significant factor in the injury rate. Crash optimization has been employed to enhance the head injury criterion value. Since the head injury criterion value is calculated from acceleration, a surrogate-model-based crash optimization method is generally used. However, when the number of design variables increases, the cost of analysis increases extremely. Conceptual design such as topology optimization is difficult to apply since it has many design variables. A crash optimization methodology that considers the head injury criterion value is proposed based on the equivalent static loads method. The proposed method calculates the head injury criterion value using the finite difference method, and the channel frequency classes filter during linear static-response structural optimization with the equivalent static loads. Two practical large-scale problems are solved to validate the proposed method. For the headform impact on the upper interior, size optimization is carried out to satisfy the constraint on the head injury criterion value while the mass is minimized. Topology optimization is performed in the case of the hood headform impact. The material distribution of the inner panel in the hood is determined to minimize the head injury criterion value.

Vehicle crash optimization considering a roof crush test and a side impact test

The vehicle performances for the side impact test and the roof crush test are dependent on the side structure design of a vehicle. Crash optimization can be employed to enhance the performances. A meta-model-based structural optimization technique is generally utilized in the optimization process since the technique is simple to use. However, the meta-model-based optimization is not suitable for problems with many design variables such as topology and topometry optimizations. A crash optimization methodology is proposed to consider both the side impact test and the roof crush test. The equivalent static loads method is adopted for the side impact test and the enforced displacement method is adopted for the roof crush test, and the two methods are integrated. A design formulation is defined. The survival distance from the side impact test and the roof strength for the roof crush test are used for the design constraints. Crash optimization is performed for a practical large-scale structure. For conceptual design, reinforcement of the B-pillar is determined by using topometry optimization, and size and shape optimizations are employed for a detailed design to satisfy the design constraints while the mass is reduced.

Non-linear dynamic response structural optimization for frontal-impact and side-impact crash tests

Vehicle crash optimization is a representative non-linear dynamic response structural optimization that utilizes highly non-linear vehicle crash analysis in the time domain. In the automobile industries, crash optimization is employed to enhance the crashworthiness characteristics. The equivalent-static-loads method has been developed for such non-linear dynamic response structural optimization. The equivalent static loads are the static loads that generate the same displacement field in linear static analysis as those of non-linear dynamic analysis at a certain time step, and the equivalent static loads are imposed as external loads in linear static structural optimization. In this research, the conventional equivalent-static-loads method is expanded to the crash management system with regard to the frontal-impact test and a full-scale vehicle for a side-impact crash test. Crash analysis frequently considers unsupported systems which do not have boundary conditions and where adjacent structures do not penetrate owing to contact. Since the equivalent-static-loads method uses linear static response structural optimization, boundary conditions are required, and the impenetrability condition cannot be directly considered. To overcome the difficulties, a problem without boundary conditions is solved by using the inertia relief method. Thus, relative displacements with respect to a certain reference point are used in linear static response optimization. The impenetrability condition in non-linear analysis is transformed to the impenetrability constraints in linear static response optimization.